a phone is on sale for 15% off the original price.part B. let p represent the original price of the phone. sales tax is 6%. using only one term, write an expression to represent the discounted price of the phone including tax.

The minimum score required for admission to the university is approximately 30.117 on the ACT Composite scale.

To find the minimum score required for admission to the university, we need to determine the cutoff score that corresponds to the top 45% of ACT Composite scores.

First, we can convert the top 45% to a z-score, which represents the number of standard deviations above or below the mean. We can use a standard normal distribution table or a calculator to find the z-score associated with the cumulative probability of 0.45.

Using the standard normal distribution table, we find that the z-score associated with a cumulative probability of 0.45 is approximately 1.645.

Next, we can use the z-score formula to calculate the minimum score required for admission:

z = (x - μ) / σ

Where:

z is the z-score

x is the ACT Composite score

μ is the mean of the scores

σ is the standard deviation of the scores

Rearranging the formula to solve for x (the ACT Composite score):

x = z * σ + μ

Substituting the known values into the equation:

x = 1.645 * 5.4 + 21.2

Calculating this expression:

x ≈ 30.117

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Answer:

(\(a^{2}\) + 9 ) × (2\(a^{2}\) + 1)

for the first one try two but im not sure

Answer: 66

Step-by-step explanation:

11 beats in 6 seconds means you mulitiply the beats times the seconds

Answer:

x≈ 100

Step-by-step explanation:

Given the equation

5x-496=1.34...

We are to find the value of x to the nearest whole number

Add 496 to both sides

5x-496+496 = 1.34+496

5x = 497.34

x = 497.34/5

x = 99.468

x ≈ 100

Hence the value of x to nearest whole number is 100

Answer:

Step-by-step explanation:

R = 1.52

H = 2.2

π = 3.14

\(V=\frac13\pi R^2\cdot H\\\\V=\frac13\cdot3.14\cdot(1.52)^2\cdot2.2=5.3200810\overline6\approx5.32\)

Answer:

p = \(\frac{16}{q+1}\)

Step-by-step explanation:

Since there are 2 equal roots then the value of the discriminant is zero, that is

b² - 4ac = 0

Given

(q + 1)x² - 8x + p = 0 ← in standard form

with a = q + 1, b = - 8, c = p , then

(- 8)² - 4p(q + 1) = 0

64 - 4p(q + 1) = 0 ( subtract 64 from both sides )

- 4p(q + 1) = - 64 ( divide both sides by - 4 )

p(q + 1) = 16 ( divide both sides by q + 1 )

p = \(\frac{16}{q+1}\)

Answer:

2x + 3 something 4 / frac x + 8

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Whatever the highest exponent is determines the degree.

The 98% confidence interval for the number of chocolate chips per cookie in Big Chip cookies is approximately 13.5529 to 15.0471 chips.

To find the 98% confidence interval for the number of chocolate chips per cookie in Big Chip cookies, we'll use the t-distribution since the sample size is relatively small (n = 61) and we don't know the population standard deviation.

The formula for the confidence interval is:

\(CI = \bar X \pm t_{critical} \times \dfrac{s } {\sqrt{n}}\)

where:

X is the sample mean,

\(t_{critical\) is the critical value for the t-distribution corresponding to the desired confidence level (98% in this case),

s is the sample standard deviation,

n is the sample size.

First, let's find the critical value for the t-distribution at a 98% confidence level with (n-1) degrees of freedom (df = 61 - 1 = 60). You can use a t-table or a calculator to find this value. For a two-tailed 98% confidence level, the critical value is approximately 2.660.

Given data:

X (sample mean) = 14.3

s (sample standard deviation) = 2.2

n (sample size) = 61

\(t_{critical\) = 2.660 (from the t-distribution table)

Now, calculate the confidence interval:

\(CI = 14.3 \pm 2.660 \times \dfrac{2.2} { \sqrt{61}}\\CI = 14.3 \pm 2.660 \times \dfrac{2.2} { 7.8102}\\CI = 14.3 \pm 0.7471\)

Lower bound = 14.3 - 0.7471 ≈ 13.5529

Upper bound = 14.3 + 0.7471 ≈ 15.0471

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Answer:

(-4, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

-3x - 3y = 3

y = -5x - 17

Step 2: Solve for x

Substitution

Step 3: Solve for y

a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.

b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.

c) Player 1 has infinitely many strategies.

d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.

e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.

Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.

Finding Nash Equilibrium

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The volume of the given rectangular prism is 396 cubic kilometer.

From the given figure,

Length = 9 km, Breadth=4 km and Height=11 km

We know that, the formula to find the volume of a rectangular prism is Length×Breadth×Height.

Here, volume = 9×4×11

= 396 cubic kilometer

Therefore, the volume of the given rectangular prism is 396 cubic kilometer.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the volume of the figure. Round your answers to the nearest hundredth, if necessary. (Figure is attached below).

Answer:

$240 extra

Step-by-step explanation:

1/3(7200) + 12(420) = 2400 + 5040 = 7440

7440 - 7200 = 240

The customer had to pay 1720 extra.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A car is priced at $7200.

If the deposit is one third = 7200/3

                                          = 240

The amount after 12 payments will be

= 240 x 12

= 2880

total cost will be

= 2880 + 2400

= 5280

and, The customer had to pay extra amount

= 7200 - 5280

= 1720

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Answer:

y= -6x - 15

Step-by-step explanation:

First you need to plug in the x and y coordinates into the equation y = -6x and you should get (-3) = -6(-2). Then you do -6 x -2 which is 12 then subtract 12 from -3 and get -15.

Just took the exam and the answer is c :)

To solve these problems, we can use the equations of motion under constant acceleration.

a. To find the time the fish has to swim away, we need to determine the time it takes for the first gannet to reach the water. We can use the equation:

y = y0 + v0t + (1/2)at^2

where:

y = final displacement (distance traveled by the bird) = -100 feet

y0 = initial displacement (initial height of the bird) = 0 feet

v0 = initial velocity of the bird = -88 feet per second

a = acceleration (due to gravity) = -32.2 feet per second squared

t = time

Plugging in the values into the equation and solving for t:

-100 = 0 + (-88)t + (1/2)(-32.2)t^2

Simplifying the equation:

-100 = -88t - 16.1t^2

Rearranging the equation:

16.1t^2 + 88t - 100 = 0

Solving this quadratic equation using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / (2a)

Here, a = 16.1, b = 88, and c = -100. Plugging in the values:

t = (-88 ± sqrt(88^2 - 4(16.1)(-100))) / (2(16.1))

Calculating the values under the square root:

t = (-88 ± sqrt(7744 + 6448)) / 32.2

t = (-88 ± sqrt(14192)) / 32.2

t ≈ (-88 ± 119.13) / 32.2

We take the positive value since time cannot be negative:

t ≈ (-88 + 119.13) / 32.2

t ≈ 31.13 / 32.2

t ≈ 0.966 seconds

Therefore, the fish has approximately 0.966 seconds to swim away.

b. Now let's analyze the second gannet's situation. The initial height of the second gannet is 84 feet, and its initial velocity is -70 feet per second. We can use the same equation of motion to find the time it takes for this gannet to reach the water:

-100 = 84 + (-70)t + (1/2)(-32.2)t^2

Simplifying the equation:

-184 = -70t - 16.1t^2

Rearranging the equation:

16.1t^2 + 70t - 184 = 0

We can solve this quadratic equation using the quadratic formula as we did before:

t = (-70 ± sqrt(70^2 - 4(16.1)(-184))) / (2(16.1))

Calculating the values under the square root:

t = (-70 ± sqrt(4900 + 11824)) / 32.2

t = (-70 ± sqrt(16724)) / 32.2

t ≈ (-70 ± 129.38) / 32.2

We take the positive value:

t ≈ (-70 + 129.38) / 32.2

t ≈ 59.38 / 32.2

t ≈ 1.844 seconds

Therefore, the second gannet takes approximately 1.844 seconds to reach the water.

Comparing the times, we find that the first gannet takes around 0.966 seconds, while the second gannet takes approximately

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The true statements are:a. Angle R is congruent to angle R'

b. (P' * Q')/(PQ) = 4

e. (C * Q')/(CQ) = 4

To determine which statements are true about triangle PQR and its image P' * Q' * R' after dilation, let's analyze each statement:

a. Angle R is congruent to angle R': This statement is true. When a triangle is dilated, the corresponding angles remain congruent.

b. (P' * Q')/(PQ) = 4: This statement is true. The scale factor of dilation is 4, which means the corresponding side lengths are multiplied by 4. Therefore, (P' * Q')/(PQ) = 4.

c. (QR)/(Q' * R') = 4: This statement is false. The scale factor of dilation applies to individual side lengths, not ratios of side lengths. Therefore, (QR)/(Q' * R') will not necessarily be equal to 4.

d. (C * P')/(CP) = 5: This statement is false. The scale factor of dilation is 4, not 5. Therefore, (C * P')/(CP) will not be equal to 5.

e. (C * Q')/(CQ) = 4: This statement is true. The scale factor of dilation is 4, so the corresponding side lengths are multiplied by 4. Therefore, (C * Q')/(CQ) = 4.

f. (C * P')/(CP) = (C * R')/(CR): This statement is false. The dilation does not guarantee that the ratios of the distances from the center C to the vertices will be equal.

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Answer:

14<x<20

Step-by-step explanation:

14<x<20 is your required answer

The option is B. Emerson is painting the outside of a cube for a math project. he knows the area of each face is 145 square inches.

the place is the quantity that expresses the quantity of vicinity on the plane or on a curved floor. The area of a plane vicinity or aircraft location refers to the area of a shape or planar lamina, while surface location refers to the region of an open floor or the boundary of a three-dimensional object. the place can be understood as the quantity of material with a given thickness that might be necessary to fashion a model of the shape, or the amount of paint essential to cowl the surface with a single coat. it's by far the 2-dimensional analog of the period of a curve (a one-dimensional concept) or the volume of a stable (a three-dimensional idea).

The region of a form can be measured by using comparing the form to squares of a set size. within the global system of devices (SI), the standard unit of the region is the rectangular meter (written as m²), which is the place of a rectangular whose aspects are one meter long. A shape with an area of 3 square meters might have an equal area to 3 such squares. In mathematics, the unit square is defined to have area one, and the place of some other form or floor is a dimensionless real number.

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Answer:length=10 width =5 Perimeter =30

Step-by-step explanation:

Area =LxW

If area is 50cm^2 and length is 5cm more than The width then the length must be 10cm. Now divide the area by the length to get width. 50/10=5 which is the width.

The formula for perimeter is P=2L+2W

P=2(10)+2(5)

P=30

a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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The required value of x, y and z are 18, 9√6/2, 9√6/2.

Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.

We have twp triangles

In upper triangle; by Pythagoras theorem

tan(30°) = 9/Base

1/\(\sqrt{3}\) = 9/Base

Base = 9√3

And

sin(30°) = 9/z

1/2 = 9/z

z = 18 units

in lower tirangle

sin(45°) = y/9√3

1/√2 =  y/9√3

y = 9√6/2

And

Cos(45°) = x/9√3

1/√2 = x/9√3

x =  9√6/2

Thus, required value of x, y and z are 18, 9√6/2, 9√6/2.

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Santiago's total savings account balance after 4 years will be total Amount = Principal + Simple Interest = $522.

Santiago's savings account balance after 4 years with 5% simple interest

After 4 years, Santiago's savings account will have a balance of $522.

To calculate this, we can use the simple interest formula:

Simple Interest = (Principal * Rate * Time)/100

Here, Santiago's principal amount is $450, the rate of interest is 5%, and the time period is 4 years.

Plugging these values into the formula:

Simple Interest = (450 * 5 * 4)/100 = $90

So, Santiago's total savings account balance after 4 years will be:

Total Amount = Principal + Simple Interest = $450 + $90 = $522.

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Answer:

k= 7

Step-by-step explanation:

First let's add like terms: a+b+a=c: a²+b=c

k+9+5=21

k+14=21

Subtract 14 from both sides of the equation

k+14-14=21-14

K=7

Hi!

\(\tt{9+k+5=21}\)

Step 1: Combine like terms.

\(\tt{9+5+k=21}\)

\(\tt{14+k=21}\)

Step 2: Subtract 14 from both sides.

\(\tt{k=7}\) \(\checkmark\)

Have a great day!

Hope that helps. :)

-Stargazing & daydreaming -

Answer:

294

Step-by-step explanation:

divide 84 by 4 to get how many miles they travel per hour, then multiply by 14 hours

Answer:

294

Step-by-step explanation:

first you will multiply 84 by 14 and divide by 4

Answer:

35

Step-by-step explanation:

Answer:

Wouldn't the area be 42?

Answer:

A or D is the answers for the question

Step-by-step explanation:

please give me brainlest and follow me

Answer:

a no.

Step-by-step explanation:

because it is clearly shown that the angle is 85 degrees

for extra informations

An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). ... Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.